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so <- qs::qread("~/Desktop/analysis/snRNASeq_metabolic_changes_in_neurons_of_hippocampus/results/seurat_obj_int_harmony.clustering_osi_annotated_clean.qs")
Registered S3 method overwritten by 'data.table':
method from
print.data.table
Registered S3 method overwritten by 'htmlwidgets':
method from
print.htmlwidget tools:rstudio
so <- so@assays$RNA@layers$counts
var(counts |> as.vector())
[1] 3.027899
mean(counts |> as.vector())
[1] 0.172479
print(nb_params_df)
Error: object 'nb_params_df' not found
library(Matrix)
library(MASS)
library(ggplot2)
# Suppose 'counts' is your dgCMatrix (genes x cells)
# Optionally, filter out genes with very low total counts:
min_total <- 10
gene_totals <- rowSums(counts)
keep_genes <- gene_totals >= min_total
counts_filtered <- counts[keep_genes, ]
gene_names <- rownames(counts_filtered)
# Initialize a data frame to collect the NB parameters and GoF statistic per gene:
results <- data.frame(Gene = character(),
mu = numeric(),
size = numeric(),
chi_sq = numeric(),
df = numeric(),
p_value = numeric(),
stringsAsFactors = FALSE)
for (i in seq_len(nrow(counts_filtered))) {
gene_counts <- as.vector(counts_filtered[i, ])
# Skip genes with no variability
if (all(gene_counts == 0)) next
fit <- try(fitdistr(gene_counts, densfun = "Negative Binomial"), silent = TRUE)
if (inherits(fit, "try-error")) next
size_est <- fit$estimate["size"]
mu_est <- fit$estimate["mu"]
total_cells <- length(gene_counts)
max_count <- max(gene_counts)
counts_seq <- 0:max_count
# Build the observed frequency vector without expanding the full data:
observed_freq <- numeric(max_count + 1)
# Zeros (not stored explicitly in the sparse matrix)
observed_freq[1] <- total_cells - sum(gene_counts > 0)
if(max_count > 0) {
observed_freq[-1] <- tabulate(gene_counts[gene_counts > 0], nbins = max_count)
}
# Calculate the expected probabilities and frequencies based on the NB model
fitted_probs <- dnbinom(counts_seq, size = size_est, mu = mu_est)
expected_freq <- fitted_probs * total_cells
# Ensure expected frequencies are nonzero for chi-square computation:
# (Sometimes, you may wish to combine bins with very low expected counts.)
# For simplicity, we assume expected_freq are > 0.
chi_sq <- sum((observed_freq - expected_freq)^2 / expected_freq)
# Degrees of freedom:
# Number of bins minus the number of estimated parameters (here 2) minus 1.
df <- length(observed_freq) - 2 - 1
# Compute p-value from the chi-square distribution:
p_val <- pchisq(chi_sq, df = df, lower.tail = FALSE)
# Append results to the dataframe:
results <- rbind(results, data.frame(Gene = gene_names[i],
mu = mu_est,
size = size_est,
chi_sq = chi_sq,
df = df,
p_value = p_val,
stringsAsFactors = FALSE))
}
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producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs produced
# View the summarized results:
print(results)
# Determine how many genes have an acceptable fit:
acceptable_fit <- sum(results$p_value > 0.05, na.rm=TRUE)
total_genes_fitted <- nrow(results)
cat("Proportion of genes well fit by NB:", acceptable_fit / total_genes_fitted, "\n")
Proportion of genes well fit by NB: 0.1103943
library(dplyr)
results %>% filter(!is.nan(p_value))
# Load necessary libraries
library(ggplot2)
library(dplyr)
# Assume nb_params_df already exists. Here is a simulated example:
# For demonstration, we'll create a small example dataframe.
set.seed(42)
reults.red <- results %>% filter(!is.nan(p_value))
nb_params_df <- reults.red
# 1. Summary Statistics for Goodness-of-Fit
summary_stats <- nb_params_df %>%
summarise(
total_genes = n(),
mean_p_value = mean(p_value),
median_p_value = median(p_value),
prop_good_fit = mean(p_value > 0.05) # proportion with p > 0.05
)
print(summary_stats)
# 2. Histogram of the p-values
p_hist <- ggplot(nb_params_df, aes(x = p_value)) +
geom_histogram(binwidth = 0.05, fill = "skyblue", color = "black", boundary = 0) +
labs(title = "Distribution of Goodness-of-Fit p-values",
x = "p-value",
y = "Number of Genes") +
theme_minimal()
print(p_hist)
# 3. Scatter Plot: p-value vs. estimated mean (mu)
p_mu <- ggplot(nb_params_df, aes(x = mu, y = p_value)) +
geom_point(color = "darkgreen", alpha = 0.7) +
geom_hline(yintercept = 0.05, linetype = "dashed", color = "red") +
labs(title = "p-value vs. Estimated Mean (mu)",
x = "Estimated mean (mu)",
y = "p-value") +
theme_minimal()
print(p_mu)
# 4. Scatter Plot: p-value vs. size parameter (dispersion)
p_size <- ggplot(nb_params_df, aes(x = size, y = p_value)) +
geom_point(color = "purple", alpha = 0.7) +
geom_hline(yintercept = 0.05, linetype = "dashed", color = "red") +
labs(title = "p-value vs. Estimated Dispersion Parameter (size)",
x = "Estimated Dispersion (size)",
y = "p-value") +
theme_minimal()
print(p_size)
# 5. Optionally, you may also examine a combined plot
library(gridExtra)
grid.arrange(p_hist + scale_y_sqrt(), p_mu + scale_y_sqrt(), p_size + scale_y_sqrt(), ncol=1)
NA
NA
NA
NA
NA
library(Matrix)
library(MASS)
library(ggplot2)
# Suppose 'counts' is your dgCMatrix (genes x cells)
# Optionally, filter out genes with very low total counts:
min_total <- 10
gene_totals <- rowSums(counts)
keep_genes <- gene_totals >= min_total
counts_filtered <- counts[keep_genes, ]
gene_names <- rownames(counts_filtered)
# Initialize a data frame to collect the NB parameters and GoF statistic per gene:
results <- data.frame(Gene = character(),
mu = numeric(),
size = numeric(),
chi_sq = numeric(),
df = numeric(),
p_value = numeric(),
stringsAsFactors = FALSE)
for (i in seq_len(nrow(counts_filtered))) {
gene_counts <- as.vector(counts_filtered[i, ])
# Skip genes with no variability
if (all(gene_counts == 0)) next
fit <- try(fitdistr(gene_counts, densfun = "Poisson"), silent = TRUE)
if (inherits(fit, "try-error")) next
size_est <- fit$estimate["size"]
mu_est <- fit$estimate["mu"]
total_cells <- length(gene_counts)
max_count <- max(gene_counts)
counts_seq <- 0:max_count
# Build the observed frequency vector without expanding the full data:
observed_freq <- numeric(max_count + 1)
# Zeros (not stored explicitly in the sparse matrix)
observed_freq[1] <- total_cells - sum(gene_counts > 0)
if(max_count > 0) {
observed_freq[-1] <- tabulate(gene_counts[gene_counts > 0], nbins = max_count)
}
# Calculate the expected probabilities and frequencies based on the NB model
fitted_probs <- dnbinom(counts_seq, size = size_est, mu = mu_est)
expected_freq <- fitted_probs * total_cells
# Ensure expected frequencies are nonzero for chi-square computation:
# (Sometimes, you may wish to combine bins with very low expected counts.)
# For simplicity, we assume expected_freq are > 0.
chi_sq <- sum((observed_freq - expected_freq)^2 / expected_freq)
# Degrees of freedom:
# Number of bins minus the number of estimated parameters (here 2) minus 1.
df <- length(observed_freq) - 2 - 1
# Compute p-value from the chi-square distribution:
p_val <- pchisq(chi_sq, df = df, lower.tail = FALSE)
# Append results to the dataframe:
results <- rbind(results, data.frame(Gene = gene_names[i],
mu = mu_est,
size = size_est,
chi_sq = chi_sq,
df = df,
p_value = p_val,
stringsAsFactors = FALSE))
}
Error in data.frame(Gene = gene_names[i], mu = mu_est, size = size_est, :
row names contain missing values
# Load required libraries
library(MASS)
library(fitdistrplus)
library(Matrix)
library(ggplot2)
library(reshape2)
# --- Step 1: Prepare the Data from dgCMatrix ---
# Suppose 'counts' is your dgCMatrix from Seurat.
# Example:
# counts <- GetAssayData(seurat_obj, slot = "counts")
# Calculate total entries, zeros, and summarize non-zero entries
total_entries <- nrow(counts) * ncol(counts)
nonzero_entries <- length(counts@x)
zero_entries <- total_entries - nonzero_entries
mean_nonzero <- mean(counts@x)
var_nonzero <- var(counts@x)
cat("Total entries:", total_entries, "\n")
Total entries: 37027800
cat("Non-zero entries:", nonzero_entries, "\n")
Non-zero entries: 2282976
cat("Zero entries:", zero_entries, "\n")
Zero entries: 34744824
cat("Mean (non-zero):", mean_nonzero, "\n")
Mean (non-zero): 2.797453
cat("Variance (non-zero):", var_nonzero, "\n")
Variance (non-zero): 41.76656
# Determine maximum observed count (from non-zeros)
max_count <- max(counts@x)
# Create a frequency vector for counts 0 to max_count
freq <- numeric(max_count + 1)
freq[1] <- zero_entries # zero count
freq[-1] <- tabulate(counts@x, nbins = max_count)
names(freq) <- 0:max_count
print(freq)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
34744824 1593557 272936 99533 55921 39057 29635 24303 20063 16819 14577 12380 10814 9322 8026 7009 6275 5409 4917
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
4286 3779 3283 3053 2746 2445 2215 2041 1824 1720 1557 1402 1372 1242 1075 988 942 894 856
38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
751 748 685 671 605 543 596 466 491 451 387 411 370 346 346 316 325 296 259
57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
253 218 212 186 199 192 171 164 145 178 140 131 143 127 105 119 105 94 112
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94
110 93 95 86 80 83 56 64 66 64 56 64 56 42 56 58 64 53 53
95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113
41 49 42 48 32 39 41 40 29 38 28 36 21 29 25 30 19 25 25
114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132
20 22 24 28 22 17 25 21 16 15 10 16 15 17 11 14 10 10 15
133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151
7 7 12 14 8 13 8 9 7 12 9 8 5 4 8 7 10 13 8
152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170
6 3 11 2 7 5 5 4 3 4 3 4 1 5 9 5 2 6 4
171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189
2 2 4 5 5 1 3 1 1 3 3 3 3 4 2 1 1 2 2
190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208
2 5 1 1 1 1 1 4 2 2 0 0 0 0 2 1 3 1 0
209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227
0 0 1 0 2 1 0 2 2 1 1 2 0 2 1 2 1 0 0
228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246
2 1 0 1 0 3 0 3 0 1 1 0 1 1 1 0 0 0 0
247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265
0 3 0 1 0 2 0 0 0 0 0 1 0 0 0 0 0 0 0
266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284
0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0
285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398
0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
418 419
0 1
# (Optional) Reconstruct a full vector from freq if memory allows (for fitting/testing):
all_counts <- rep(0:max_count, times = freq)
# --- Step 2: Fit a Poisson Model ---
# Use fitdistr() to estimate the Poisson parameter lambda
pois_fit <- fitdistr(all_counts, densfun = "Poisson")
print(pois_fit)
lambda
1.724790e-01
(6.825024e-05)
# The Poisson parameter is "lambda"
lambda_est <- pois_fit$estimate["lambda"]
# --- Step 3: Compute Expected Frequencies Under Poisson ---
# Create a sequence of counts (from 0 to max_count)
counts_seq <- 0:max_count
# Compute Poisson PMF for each count and scale to get expected frequencies
fitted_probs <- dpois(counts_seq, lambda = lambda_est)
total_obs <- length(all_counts)
expected_freq <- fitted_probs * total_obs
# Observed frequencies (as computed above)
observed_freq <- as.numeric(table(factor(all_counts, levels = counts_seq)))
# Create a dataframe for plotting
df <- data.frame(
Count = counts_seq,
Observed = observed_freq,
Expected = expected_freq
)
# --- Step 4: Visualization with ggplot2 ---
# Melt the dataframe to long format for ggplot2
df_melted <- melt(df, id.vars = "Count", variable.name = "Type", value.name = "Frequency")
# Create the plot:
ggplot(df_melted, aes(x = Count, y = Frequency, fill = Type)) +
geom_bar(stat = "identity", position = "dodge", color = "black", alpha = 0.7) +
scale_fill_manual(values = c("Observed" = "skyblue", "Expected" = "red")) +
labs(title = "Observed vs Expected Frequencies (Poisson Fit)",
x = "Count",
y = "Frequency (square-root scale)") +
theme_minimal() +
scale_y_sqrt() +
xlim(-1, 10)
freq
[1] 1131587421 44035942 14688793 6375839 3302039 1930523 1235210 847755 612284 461604 358807 287885 234672
[14] 195140 165146 142135 123007 107416 94747 84349 75221 67761 60961 55677 50659 46293
[27] 42688 39039 35943 33414 31012 29193 26979 25303 23617 22162 20755 19271 18218
[40] 17338 16417 15374 14689 13756 13008 12486 12016 11171 10554 10080 9651 9284
[53] 8782 8379 7963 7606 7386 7065 6805 6381 6201 5973 5721 5407 5303
[66] 5241 4941 4727 4633 4324 4188 4006 3902 3868 3758 3559 3403 3272
[79] 3192 3096 2928 2902 2779 2789 2644 2569 2487 2396 2285 2229 2198
[92] 2121 2140 2044 1941 1899 1874 1797 1725 1699 1611 1653 1668 1493
[105] 1446 1438 1488 1415 1383 1344 1245 1201 1274 1171 1171 1161 1088
[118] 1039 1031 1112 993 988 997 929 933 837 914 865 872 864
[131] 812 852 750 759 753 701 737 716 639 642 673 625 628
[144] 623 652 624 582 546 561 545 559 551 521 509 512 531
[157] 456 474 421 452 448 462 453 404 429 436 368 430 395
[170] 403 397 371 340 385 379 373 340 336 298 332 328 356
[183] 312 316 291 291 279 289 301 259 288 279 277 250 234
[196] 228 239 230 251 263 227 238 211 228 226 207 216 192
[209] 215 228 187 194 198 203 212 215 204 191 167 180 174
[222] 170 189 171 169 201 158 172 185 181 157 158 164 157
[235] 152 164 149 159 137 146 140 136 148 142 139 140 140
[248] 142 131 119 135 135 125 126 123 124 138 111 118 137
[261] 117 117 119 132 111 106 114 105 128 115 113 105 94
[274] 109 92 101 105 110 99 90 92 83 98 92 94 114
[287] 74 82 97 99 94 94 75 103 82 79 66 82 105
[300] 84 80 101 90 76 82 54 70 70 66 77 77 69
[313] 71 66 68 78 58 63 80 72 73 74 69 70 71
[326] 71 86 66 57 53 62 62 61 67 64 61 70 68
[339] 59 65 63 60 59 58 62 58 72 43 52 57 57
[352] 53 55 48 51 46 51 44 56 49 64 40 39 54
[365] 58 46 33 43 46 40 40 53 46 53 50 39 43
[378] 56 42 46 44 43 37 53 48 48 46 33 34 43
[391] 46 37 40 43 37 33 42 39 27 40 42 44 43
[404] 39 46 37 43 34 25 38 39 27 27 27 33 32
[417] 28 34 37 33 28 25 29 24 29 35 25 27 38
[430] 24 33 22 26 24 26 29 39 17 32 22 19 26
[443] 28 19 23 31 30 21 35 34 21 25 26 40 31
[456] 17 16 32 33 16 24 23 21 22 30 27 21 21
[469] 19 30 21 25 21 24 23 28 17 26 17 24 28
[482] 25 24 20 24 21 25 22 22 15 20 21 29 19
[495] 16 21 22 21 24 23 20 27 23 30 18 18 14
[508] 15 12 20 17 22 18 17 24 17 12 15 24 17
[521] 21 16 16 20 19 15 20 26 23 17 26 17 14
[534] 12 12 17 13 14 25 13 18 17 15 18 12 18
[547] 20 16 19 15 11 17 21 17 22 19 12 23 9
[560] 8 15 17 16 16 13 12 22 9 5 16 23 7
[573] 21 14 24 17 13 18 9 13 12 11 12 14 15
[586] 12 13 17 14 14 14 13 11 14 13 11 13 20
[599] 13 13 9 15 15 17 13 17 8 12 15 17 15
[612] 16 14 13 14 11 15 7 19 15 20 15 12 15
[625] 17 9 18 12 14 18 14 14 15 12 14 15 10
[638] 12 6 12 12 19 15 17 16 14 20 11 17 10
[651] 12 13 12 12 19 12 18 10 9 13 9 19 14
[664] 11 13 21 19 15 8 11 18 18 11 14 12 16
[677] 14 14 14 20 13 11 16 17 24 17 10 16 12
[690] 8 19 11 9 13 11 19 10 9 18 12 13 8
[703] 17 14 20 12 14 4 20 20 7 12 14 9 10
[716] 16 10 7 11 8 7 15 9 13 13 14 9 12
[729] 14 16 13 16 12 9 10 10 11 5 12 10 13
[742] 8 12 16 8 11 9 12 12 13 12 9 21 10
[755] 8 14 14 11 14 5 11 10 13 18 9 13 11
[768] 17 15 15 8 12 12 14 9 14 14 12 8 12
[781] 15 16 11 12 8 18 10 9 3 15 14 12 11
[794] 10 16 16 12 8 8 15 18 6 10 13 5 13
[807] 14 7 13 9 7 12 13 10 6 9 9 10 14
[820] 20 8 9 10 12 13 12 11 14 4 10 19 8
[833] 14 0 8 12 8 9 17 9 10 10 10 8 9
[846] 7 12 10 8 7 6 11 13 9 12 6 7 13
[859] 8 12 14 8 5 10 11 8 12 6 7 13 5
[872] 13 7 10 12 15 7 8 11 10 12 11 10 13
[885] 12 5 10 9 15 10 4 9 10 14 8 8 7
[898] 9 10 7 8 5 8 8 9 10 7 11 7 10
[911] 9 6 10 5 9 6 13 6 15 7 7 8 10
[924] 15 4 6 8 9 7 9 12 6 13 6 8 9
[937] 7 5 8 10 7 12 17 7 11 5 4 9 7
[950] 11 6 7 5 8 13 11 5 11 5 7 12 14
[963] 6 5 9 9 11 14 13 5 10 5 8 9 11
[976] 3 8 11 9 8 10 7 8 8 13 9 1 9
[989] 10 8 8 5 17 10 5 11 6 9 16 9
[ reached getOption("max.print") -- omitted 3868 entries ]
library(SeuratData)
Registered S3 method overwritten by 'data.table':
method from
print.data.table
Registered S3 method overwritten by 'htmlwidgets':
method from
print.htmlwidget tools:rstudio
── Installed datasets ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── SeuratData v0.2.2.9001 ──
✔ kidneyref 1.0.2 ✔ pbmcref 1.0.0
✔ panc8 3.0.2 ✔ stxKidney 0.1.0
✔ pbmc3k 3.1.4
────────────────────────────────────────────────────────────────────────────────────── Key ─────────────────────────────────────────────────────────────────────────────────────
✔ Dataset loaded successfully
❯ Dataset built with a newer version of Seurat than installed
❓ Unknown version of Seurat installed
InstallData("pbmc3k")
Warning: The following packages are already installed and will not be reinstalled: pbmc3k
pbmc3k <- Seurat::UpdateSeuratObject(pbmc3k)
Validating object structure
Updating object slots
Ensuring keys are in the proper structure
Warning: Assay RNA changing from Assay to AssayEnsuring keys are in the proper structure
Ensuring feature names don't have underscores or pipes
Updating slots in RNA
Validating object structure for Assay ‘RNA’
Object representation is consistent with the most current Seurat version
counts <- pbmc3k@assays$RNA@counts